MinT - Best Known (36, 77, s)-Nets in Base 27

Best Known (36, 77, s)-Nets in Base 27

(36, 77, 170)-Net over F₂₇ — Constructive and digital

Digital (36, 77, 170)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (7, 27, 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 (9, 50, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(36, 77, 348)-Net over F₂₇ — Digital

Digital (36, 77, 348)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(36, 77, 370)-Net in Base 27 — Constructive

(36, 77, 370)-net in base 27, using

3 times m-reduction [i] based on (36, 80, 370)-net in base 27, using
- base change [i] based on digital (16, 60, 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]

(36, 77, 87793)-Net in Base 27 — Upper bound on s

There is no (36, 77, 87794)-net in base 27, because

1 times m-reduction [i] would yield (36, 76, 87794)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 6 076520 538139 679570 032005 222664 623074 617328 567287 746509 125195 479863 818725 372847 933811 459799 664017 031157 638857 > 27⁷⁶ [i]