MinT - Best Known (12, 12+65, s)-Nets in Base 128

Best Known (12, 12+65, s)-Nets in Base 128

(12, 12+65, 288)-Net over F₁₂₈ — Constructive and digital

Digital (12, 77, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 77, 288)-net over F₁₂₈, using
- net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
    - a function field by SÃ©mirat [i]

(12, 12+65, 321)-Net over F₁₂₈ — Digital

Digital (12, 77, 321)-net over F₁₂₈, using

net from sequence [i] based on digital (12, 320)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 12 and N(F) ≥ 321, using
  - a curve from the manYPoints database [i]

(12, 12+65, 10163)-Net in Base 128 — Upper bound on s

There is no (12, 77, 10164)-net in base 128, because

1 times m-reduction [i] would yield (12, 76, 10164)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 14097 151486 007305 794624 830120 908071 535698 616026 322190 916990 167418 394329 425720 027188 938811 130551 961025 730576 857784 320690 811538 500820 916602 269276 809428 736990 870555 > 128⁷⁶ [i]