MinT - Best Known (225−122, 225, s)-Nets in Base 4

Best Known (225−122, 225, s)-Nets in Base 4

(225−122, 225, 104)-Net over F₄ — Constructive and digital

Digital (103, 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]

(225−122, 225, 144)-Net over F₄ — Digital

Digital (103, 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]

(225−122, 225, 1256)-Net in Base 4 — Upper bound on s

There is no (103, 225, 1257)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3046 081190 650931 910207 334189 302673 536686 041865 570596 508548 033018 153705 634552 218221 366672 551673 000423 642757 702292 146267 306523 799564 972160 > 4²²⁵ [i]