MinT - Best Known (241−137, 241, s)-Nets in Base 4

Best Known (241−137, 241, s)-Nets in Base 4

(241−137, 241, 104)-Net over F₄ — Constructive and digital

Digital (104, 241, 104)-net over F₄, using

t-expansion [i] based on digital (73, 241, 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]

(241−137, 241, 144)-Net over F₄ — Digital

Digital (104, 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]

(241−137, 241, 1107)-Net in Base 4 — Upper bound on s

There is no (104, 241, 1108)-net in base 4, because

1 times m-reduction [i] would yield (104, 240, 1108)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 259798 436481 430472 608502 659206 724446 995788 679697 876440 453664 020682 887151 958340 779657 829667 049465 776311 656532 598488 454367 517804 030669 883073 145380 > 4²⁴⁰ [i]