MinT - Best Known (250−149, 250, s)-Nets in Base 4

Best Known (250−149, 250, s)-Nets in Base 4

(250−149, 250, 104)-Net over F₄ — Constructive and digital

Digital (101, 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]

(250−149, 250, 144)-Net over F₄ — Digital

Digital (101, 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]

(250−149, 250, 944)-Net in Base 4 — Upper bound on s

There is no (101, 250, 945)-net in base 4, because

1 times m-reduction [i] would yield (101, 249, 945)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 872950 751980 210645 322496 033091 360867 092287 221184 138387 233469 587606 538494 709375 828573 670958 782254 492999 187616 256150 969349 939036 481763 086068 237786 749392 > 4²⁴⁹ [i]