MinT - Best Known (126−82, 126, s)-Nets in Base 16

Best Known (126−82, 126, s)-Nets in Base 16

(126−82, 126, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 126, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 126, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(126−82, 126, 226)-Net over F₁₆ — Digital

Digital (44, 126, 226)-net over F₁₆, using

t-expansion [i] based on digital (43, 126, 226)-net over F₁₆, using
- net from sequence [i] based on digital (43, 225)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 43 and N(F) ≥ 226, using
    - Drinfeld modules of rank 1 [i]

(126−82, 126, 5375)-Net in Base 16 — Upper bound on s

There is no (44, 126, 5376)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 52 384322 852504 256005 067226 775910 051522 724702 883107 046676 003360 287269 515981 519061 098295 982965 317982 308359 897572 390731 120118 500335 418445 836281 596278 243241 > 16¹²⁶ [i]