MinT - Best Known (260−154, 260, s)-Nets in Base 4

Best Known (260−154, 260, s)-Nets in Base 4

(260−154, 260, 130)-Net over F₄ — Constructive and digital

Digital (106, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(260−154, 260, 144)-Net over F₄ — Digital

Digital (106, 260, 144)-net over F₄, using

t-expansion [i] based on digital (91, 260, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(260−154, 260, 998)-Net in Base 4 — Upper bound on s

There is no (106, 260, 999)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 668685 627659 728468 734187 998975 347203 226415 254289 699054 759617 244612 787983 853443 171997 575986 226232 500348 788089 676338 778798 847262 747339 550059 159962 460551 865720 > 4²⁶⁰ [i]