MinT - Best Known (253−125, 253, s)-Nets in Base 4

Best Known (253−125, 253, s)-Nets in Base 4

(253−125, 253, 130)-Net over F₄ — Constructive and digital

Digital (128, 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]

(253−125, 253, 184)-Net over F₄ — Digital

Digital (128, 253, 184)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(253−125, 253, 2182)-Net in Base 4 — Upper bound on s

There is no (128, 253, 2183)-net in base 4, because

1 times m-reduction [i] would yield (128, 252, 2183)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 899765 525124 872385 929806 723171 778977 443204 822079 956339 327977 446021 323154 537014 776829 811982 085614 870846 179230 036445 620064 103792 329061 488971 810053 799600 > 4²⁵² [i]