MinT - Best Known (101, 101+137, s)-Nets in Base 4

Best Known (101, 101+137, s)-Nets in Base 4

(101, 101+137, 104)-Net over F₄ — Constructive and digital

Digital (101, 238, 104)-net over F₄, using

t-expansion [i] based on digital (73, 238, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(101, 101+137, 144)-Net over F₄ — Digital

Digital (101, 238, 144)-net over F₄, using

t-expansion [i] based on digital (91, 238, 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]

(101, 101+137, 1038)-Net in Base 4 — Upper bound on s

There is no (101, 238, 1039)-net in base 4, because

1 times m-reduction [i] would yield (101, 237, 1039)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 50760 280687 165756 251719 932372 780915 662214 237455 387137 621613 074627 250507 588796 659115 284546 194122 237401 700014 478751 352146 618056 663347 940114 635760 > 4²³⁷ [i]