MinT - Best Known (99−83, 99, s)-Nets in Base 27

Best Known (99−83, 99, s)-Nets in Base 27

(99−83, 99, 96)-Net over F₂₇ — Constructive and digital

Digital (16, 99, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 99, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(99−83, 99, 144)-Net over F₂₇ — Digital

Digital (16, 99, 144)-net over F₂₇, using

net from sequence [i] based on digital (16, 143)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 16 and N(F) ≥ 144, using
  - a curve from the manYPoints database [i]

(99−83, 99, 1616)-Net in Base 27 — Upper bound on s

There is no (16, 99, 1617)-net in base 27, because

1 times m-reduction [i] would yield (16, 98, 1617)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 191 398665 525402 589609 515531 106853 484417 729406 033567 324123 535168 922053 330700 626788 488213 422986 315626 076016 050565 952272 797154 418259 366633 600859 > 27⁹⁸ [i]