MinT - Best Known (98, 247, s)-Nets in Base 4

Best Known (98, 247, s)-Nets in Base 4

(98, 247, 104)-Net over F₄ — Constructive and digital

Digital (98, 247, 104)-net over F₄, using

t-expansion [i] based on digital (73, 247, 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]

(98, 247, 144)-Net over F₄ — Digital

Digital (98, 247, 144)-net over F₄, using

t-expansion [i] based on digital (91, 247, 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]

(98, 247, 889)-Net in Base 4 — Upper bound on s

There is no (98, 247, 890)-net in base 4, because

1 times m-reduction [i] would yield (98, 246, 890)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13466 192945 932246 106805 949859 824115 600832 462817 351600 969215 489596 792940 083203 475939 563899 275289 016720 020100 248155 715148 495125 824172 442200 492950 065216 > 4²⁴⁶ [i]