MinT - Best Known (175−69, 175, s)-Nets in Base 4

Best Known (175−69, 175, s)-Nets in Base 4

(175−69, 175, 130)-Net over F₄ — Constructive and digital

Digital (106, 175, 130)-net over F₄, using

t-expansion [i] based on digital (105, 175, 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]

(175−69, 175, 273)-Net over F₄ — Digital

Digital (106, 175, 273)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−69, 175, 5410)-Net in Base 4 — Upper bound on s

There is no (106, 175, 5411)-net in base 4, because

1 times m-reduction [i] would yield (106, 174, 5411)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 574 123726 700561 167348 578551 903647 514056 924376 443768 981265 398239 942461 312256 857349 076523 823893 293352 031745 > 4¹⁷⁴ [i]