MinT - Best Known (235−103, 235, s)-Nets in Base 4

Best Known (235−103, 235, s)-Nets in Base 4

(235−103, 235, 130)-Net over F₄ — Constructive and digital

Digital (132, 235, 130)-net over F₄, using

t-expansion [i] based on digital (105, 235, 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]

(235−103, 235, 251)-Net over F₄ — Digital

Digital (132, 235, 251)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−103, 235, 3787)-Net in Base 4 — Upper bound on s

There is no (132, 235, 3788)-net in base 4, because

1 times m-reduction [i] would yield (132, 234, 3788)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 766 766552 969437 294279 400762 366017 389262 967073 278074 426433 142996 752709 609262 739728 412733 436548 374459 610913 394547 431332 227362 591342 895264 613300 > 4²³⁴ [i]