MinT - Best Known (75−38, 75, s)-Nets in Base 16

Best Known (75−38, 75, s)-Nets in Base 16

(75−38, 75, 257)-Net over F₁₆ — Constructive and digital

Digital (37, 75, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(37,256) in PG(74,16)) for nets [i] based on digital (0, 38, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(75−38, 75, 269)-Net over F₁₆ — Digital

Digital (37, 75, 269)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−38, 75, 29928)-Net in Base 16 — Upper bound on s

There is no (37, 75, 29929)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 038079 227630 808973 336793 094221 578218 706116 424713 936835 411516 674501 774719 213496 586031 032016 > 16⁷⁵ [i]