MinT - Best Known (250−134, 250, s)-Nets in Base 4

Best Known (250−134, 250, s)-Nets in Base 4

(250−134, 250, 130)-Net over F₄ — Constructive and digital

Digital (116, 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]

(250−134, 250, 168)-Net over F₄ — Digital

Digital (116, 250, 168)-net over F₄, using

t-expansion [i] based on digital (115, 250, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(250−134, 250, 1461)-Net in Base 4 — Upper bound on s

There is no (116, 250, 1462)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 334985 335676 843003 111639 617835 123957 411020 617576 924557 874657 296785 927753 564780 961157 014239 479410 978544 610448 136006 132924 485549 540014 208805 817521 700900 > 4²⁵⁰ [i]