MinT - Best Known (225−97, 225, s)-Nets in Base 4

Best Known (225−97, 225, s)-Nets in Base 4

(225−97, 225, 130)-Net over F₄ — Constructive and digital

Digital (128, 225, 130)-net over F₄, using

t-expansion [i] based on digital (105, 225, 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]

(225−97, 225, 255)-Net over F₄ — Digital

Digital (128, 225, 255)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−97, 225, 3990)-Net in Base 4 — Upper bound on s

There is no (128, 225, 3991)-net in base 4, because

1 times m-reduction [i] would yield (128, 224, 3991)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 731 774704 629175 492419 445647 947387 772556 001000 976595 781184 190290 113063 874889 221462 280495 104370 410422 641417 212713 449263 873546 564586 872076 > 4²²⁴ [i]