MinT - Best Known (128−84, 128, s)-Nets in Base 16

Best Known (128−84, 128, s)-Nets in Base 16

(128−84, 128, 225)-Net over F₁₆ — Constructive and digital

Digital (44, 128, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 128, 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]

(128−84, 128, 226)-Net over F₁₆ — Digital

Digital (44, 128, 226)-net over F₁₆, using

t-expansion [i] based on digital (43, 128, 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]

(128−84, 128, 5122)-Net in Base 16 — Upper bound on s

There is no (44, 128, 5123)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 13516 249709 067331 982779 650791 671782 763018 249765 417164 524495 732656 731469 290659 036717 315575 323883 188693 545550 658112 050784 407577 734361 764038 178770 462384 121216 > 16¹²⁸ [i]