MinT - Best Known (62, 62+48, s)-Nets in Base 27

Best Known (62, 62+48, s)-Nets in Base 27

(62, 62+48, 248)-Net over F₂₇ — Constructive and digital

Digital (62, 110, 248)-net over F₂₇, using

generalized (u,Â u+v)-construction [i] based on
1. digital (7, 23, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]
2. digital (7, 31, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇ (see above)
3. digital (8, 56, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(62, 62+48, 398)-Net in Base 27 — Constructive

(62, 110, 398)-net in base 27, using

(u,Â u+v)-construction [i] based on
1. digital (0, 24, 28)-net over F₂₇, using
  - net from sequence [i] based on digital (0, 27)-sequence over F₂₇, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 0 and N(F) ≥ 28, using
      - the rational function field F₂₇(x) [i]
    - Niederreiter sequence [i]
2. (38, 86, 370)-net in base 27, using
  - 2 times m-reduction [i] based on (38, 88, 370)-net in base 27, using
    - base change [i] based on digital (16, 66, 370)-net over F₈₁, using
      - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
        a function field by GarcÃa and Quoos [i]

(62, 62+48, 1605)-Net over F₂₇ — Digital

Digital (62, 110, 1605)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+48, 1370259)-Net in Base 27 — Upper bound on s

There is no (62, 110, 1370260)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 28 185172 867505 937281 016398 363465 641678 119244 824756 319850 810581 641740 650156 721763 540687 914449 181917 204143 633496 747798 423215 964952 599864 644843 098330 851409 940033 > 27¹¹⁰ [i]