MinT - Best Known (78−63, 78, s)-Nets in Base 16

Best Known (78−63, 78, s)-Nets in Base 16

(78−63, 78, 65)-Net over F₁₆ — Constructive and digital

Digital (15, 78, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 78, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(78−63, 78, 98)-Net over F₁₆ — Digital

Digital (15, 78, 98)-net over F₁₆, using

net from sequence [i] based on digital (15, 97)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 15 and N(F) ≥ 98, using
  - a curve from the manYPoints database [i]

(78−63, 78, 793)-Net in Base 16 — Upper bound on s

There is no (15, 78, 794)-net in base 16, because

1 times m-reduction [i] would yield (15, 77, 794)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 528 535004 077646 662318 815775 363462 306423 977534 995369 280321 762042 382370 572448 234893 512713 182336 > 16⁷⁷ [i]