MinT - Best Known (250−147, 250, s)-Nets in Base 4

Best Known (250−147, 250, s)-Nets in Base 4

(250−147, 250, 104)-Net over F₄ — Constructive and digital

Digital (103, 250, 104)-net over F₄, using

t-expansion [i] based on digital (73, 250, 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]

(250−147, 250, 144)-Net over F₄ — Digital

Digital (103, 250, 144)-net over F₄, using

t-expansion [i] based on digital (91, 250, 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]

(250−147, 250, 997)-Net in Base 4 — Upper bound on s

There is no (103, 250, 998)-net in base 4, because

1 times m-reduction [i] would yield (103, 249, 998)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 868420 327252 065093 774838 310860 432496 290496 543502 813434 999570 662587 889755 754984 073547 097894 804885 619206 419030 121756 331451 605804 024029 494695 241009 794140 > 4²⁴⁹ [i]