MinT - Best Known (253−124, 253, s)-Nets in Base 4

Best Known (253−124, 253, s)-Nets in Base 4

(253−124, 253, 130)-Net over F₄ — Constructive and digital

Digital (129, 253, 130)-net over F₄, using

t-expansion [i] based on digital (105, 253, 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]

(253−124, 253, 189)-Net over F₄ — Digital

Digital (129, 253, 189)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(253−124, 253, 2233)-Net in Base 4 — Upper bound on s

There is no (129, 253, 2234)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 214 501921 642657 005650 127689 906647 908145 994320 085899 333332 735424 672194 340118 912617 712081 764446 201642 428709 359590 611455 087972 877829 656890 279229 733037 523520 > 4²⁵³ [i]