MinT - Best Known (250−138, 250, s)-Nets in Base 4

Best Known (250−138, 250, s)-Nets in Base 4

(250−138, 250, 130)-Net over F₄ — Constructive and digital

Digital (112, 250, 130)-net over F₄, using

t-expansion [i] based on digital (105, 250, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(250−138, 250, 165)-Net over F₄ — Digital

Digital (112, 250, 165)-net over F₄, using

t-expansion [i] based on digital (109, 250, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(250−138, 250, 1286)-Net in Base 4 — Upper bound on s

There is no (112, 250, 1287)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 368695 217320 098648 086749 679343 020530 187228 358392 821042 538911 655596 390237 002536 025257 954471 065443 108073 895012 183890 271635 932830 435375 240551 954034 642920 > 4²⁵⁰ [i]