MinT - Best Known (241−134, 241, s)-Nets in Base 4

Best Known (241−134, 241, s)-Nets in Base 4

(241−134, 241, 130)-Net over F₄ — Constructive and digital

Digital (107, 241, 130)-net over F₄, using

t-expansion [i] based on digital (105, 241, 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]

(241−134, 241, 144)-Net over F₄ — Digital

Digital (107, 241, 144)-net over F₄, using

t-expansion [i] based on digital (91, 241, 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]

(241−134, 241, 1204)-Net in Base 4 — Upper bound on s

There is no (107, 241, 1205)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 084119 821713 891417 635234 273821 121102 922814 224324 076198 851179 112132 809667 200416 814438 914793 130418 829087 324333 511440 961181 258061 879302 916629 706280 > 4²⁴¹ [i]