MinT - Best Known (253−123, 253, s)-Nets in Base 4

Best Known (253−123, 253, s)-Nets in Base 4

(253−123, 253, 130)-Net over F₄ — Constructive and digital

Digital (130, 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]

(253−123, 253, 193)-Net over F₄ — Digital

Digital (130, 253, 193)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(253−123, 253, 2361)-Net in Base 4 — Upper bound on s

There is no (130, 253, 2362)-net in base 4, because

1 times m-reduction [i] would yield (130, 252, 2362)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 869872 553372 102358 402480 164257 463079 052784 978932 155783 550711 503368 822088 019003 248733 263657 543665 486275 085929 657677 270363 172967 209649 959566 711277 039296 > 4²⁵² [i]