MinT - Best Known (134, 134+105, s)-Nets in Base 4

Best Known (134, 134+105, s)-Nets in Base 4

(134, 134+105, 130)-Net over F₄ — Constructive and digital

Digital (134, 239, 130)-net over F₄, using

t-expansion [i] based on digital (105, 239, 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]

(134, 134+105, 253)-Net over F₄ — Digital

Digital (134, 239, 253)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 134+105, 3797)-Net in Base 4 — Upper bound on s

There is no (134, 239, 3798)-net in base 4, because

1 times m-reduction [i] would yield (134, 238, 3798)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 196206 169102 152459 765103 865685 513333 784284 933716 384340 052668 701895 505993 840562 748016 332351 073145 100705 898060 514047 940095 603605 992602 094846 859310 > 4²³⁸ [i]