MinT - Best Known (250−112, 250, s)-Nets in Base 4

Best Known (250−112, 250, s)-Nets in Base 4

(250−112, 250, 130)-Net over F₄ — Constructive and digital

Digital (138, 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]

(250−112, 250, 248)-Net over F₄ — Digital

Digital (138, 250, 248)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−112, 250, 3480)-Net in Base 4 — Upper bound on s

There is no (138, 250, 3481)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 320429 122932 773738 327311 140434 065969 127985 087606 837459 456416 718539 054326 955709 929529 068031 690999 263993 919482 264412 209223 633104 796920 583650 336481 306748 > 4²⁵⁰ [i]