MinT - Best Known (104, 225, s)-Nets in Base 4

Best Known (104, 225, s)-Nets in Base 4

(104, 225, 104)-Net over F₄ — Constructive and digital

Digital (104, 225, 104)-net over F₄, using

t-expansion [i] based on digital (73, 225, 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]

(104, 225, 144)-Net over F₄ — Digital

Digital (104, 225, 144)-net over F₄, using

t-expansion [i] based on digital (91, 225, 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]

(104, 225, 1318)-Net in Base 4 — Upper bound on s

There is no (104, 225, 1319)-net in base 4, because

1 times m-reduction [i] would yield (104, 224, 1319)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 739 598949 070348 105374 104728 937732 395352 772679 496611 852186 777028 054601 613728 386889 126690 686457 763356 837996 187576 337889 106776 013026 241120 > 4²²⁴ [i]