MinT - Best Known (244−111, 244, s)-Nets in Base 4

Best Known (244−111, 244, s)-Nets in Base 4

(244−111, 244, 130)-Net over F₄ — Constructive and digital

Digital (133, 244, 130)-net over F₄, using

t-expansion [i] based on digital (105, 244, 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]

(244−111, 244, 231)-Net over F₄ — Digital

Digital (133, 244, 231)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−111, 244, 3206)-Net in Base 4 — Upper bound on s

There is no (133, 244, 3207)-net in base 4, because

1 times m-reduction [i] would yield (133, 243, 3207)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 202 746917 970584 224845 861964 535473 983116 555517 887228 313799 100251 430167 226867 484547 077269 963403 624340 786401 265069 980272 616333 752493 762680 584081 711840 > 4²⁴³ [i]