MinT - Best Known (249−151, 249, s)-Nets in Base 4

Best Known (249−151, 249, s)-Nets in Base 4

(249−151, 249, 104)-Net over F₄ — Constructive and digital

Digital (98, 249, 104)-net over F₄, using

t-expansion [i] based on digital (73, 249, 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]

(249−151, 249, 144)-Net over F₄ — Digital

Digital (98, 249, 144)-net over F₄, using

t-expansion [i] based on digital (91, 249, 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]

(249−151, 249, 877)-Net in Base 4 — Upper bound on s

There is no (98, 249, 878)-net in base 4, because

1 times m-reduction [i] would yield (98, 248, 878)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 209744 283871 950080 439489 935070 363413 699486 281237 793443 725847 523762 839466 582843 276485 738532 756986 753205 723670 784995 821215 669797 687906 766326 770057 325214 > 4²⁴⁸ [i]