MinT - Best Known (51, 51+59, s)-Nets in Base 16

Best Known (51, 51+59, s)-Nets in Base 16

(51, 51+59, 243)-Net over F₁₆ — Constructive and digital

Digital (51, 110, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 110, 243)-net over F₁₆, using
- net from sequence [i] based on digital (48, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
    - a function field by GarcÃa and Quoos [i]

(51, 51+59, 274)-Net over F₁₆ — Digital

Digital (51, 110, 274)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 51+59, 26097)-Net in Base 16 — Upper bound on s

There is no (51, 110, 26098)-net in base 16, because

1 times m-reduction [i] would yield (51, 109, 26098)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 177583 640050 470648 562124 437625 029622 743247 328597 375507 384478 573820 969269 831542 710783 453293 237724 028374 301761 316284 876300 939440 650856 > 16¹⁰⁹ [i]