MinT - Best Known (51, 51+64, s)-Nets in Base 16

Best Known (51, 51+64, s)-Nets in Base 16

(51, 51+64, 243)-Net over F₁₆ — Constructive and digital

Digital (51, 115, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 115, 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+64, 255)-Net over F₁₆ — Digital

Digital (51, 115, 255)-net over F₁₆, using

t-expansion [i] based on digital (50, 115, 255)-net over F₁₆, using
- net from sequence [i] based on digital (50, 254)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 50 and N(F) ≥ 255, using
    - a curve from the manYPoints database [i]

(51, 51+64, 257)-Net in Base 16

(51, 115, 257)-net in base 16, using

base change [i] based on digital (28, 92, 257)-net over F₃₂, using
- net from sequence [i] based on digital (28, 256)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 28 and N(F) ≥ 257, using
    - a curve from the manYPoints database [i]

(51, 51+64, 18099)-Net in Base 16 — Upper bound on s

There is no (51, 115, 18100)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 978462 669274 033696 756138 121199 052186 370055 859030 598229 666993 290756 606302 708605 820677 836417 661426 171822 562931 443234 476148 818643 061402 199251 > 16¹¹⁵ [i]