MinT - Best Known (174−67, 174, s)-Nets in Base 4

Best Known (174−67, 174, s)-Nets in Base 4

(174−67, 174, 130)-Net over F₄ — Constructive and digital

Digital (107, 174, 130)-net over F₄, using

t-expansion [i] based on digital (105, 174, 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]

(174−67, 174, 295)-Net over F₄ — Digital

Digital (107, 174, 295)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−67, 174, 6260)-Net in Base 4 — Upper bound on s

There is no (107, 174, 6261)-net in base 4, because

1 times m-reduction [i] would yield (107, 173, 6261)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 143 591273 723783 254822 552247 402294 741400 850538 640367 362195 695620 769918 523425 350027 308789 180301 787271 969280 > 4¹⁷³ [i]