MinT - Best Known (46, 98, s)-Nets in Base 27

Best Known (46, 98, s)-Nets in Base 27

(46, 98, 188)-Net over F₂₇ — Constructive and digital

Digital (46, 98, 188)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (10, 36, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]
2. digital (10, 62, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇ (see above)

(46, 98, 370)-Net in Base 27 — Constructive

(46, 98, 370)-net in base 27, using

t-expansion [i] based on (43, 98, 370)-net in base 27, using
- 10 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
  - base change [i] based on digital (16, 81, 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]

(46, 98, 427)-Net over F₂₇ — Digital

Digital (46, 98, 427)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 98, 100786)-Net in Base 27 — Upper bound on s

There is no (46, 98, 100787)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 187 809613 814695 528147 460130 013186 828708 869274 904357 778833 977242 651370 212031 342105 709994 513591 339571 098951 328606 694709 754868 998179 737875 373349 > 27⁹⁸ [i]