MinT - Best Known (132, 132+123, s)-Nets in Base 4

Best Known (132, 132+123, s)-Nets in Base 4

(132, 132+123, 130)-Net over F₄ — Constructive and digital

Digital (132, 255, 130)-net over F₄, using

t-expansion [i] based on digital (105, 255, 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]

(132, 132+123, 200)-Net over F₄ — Digital

Digital (132, 255, 200)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 132+123, 2473)-Net in Base 4 — Upper bound on s

There is no (132, 255, 2474)-net in base 4, because

1 times m-reduction [i] would yield (132, 254, 2474)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 843 057368 038976 138746 029881 876898 021016 693020 747556 700502 133158 773304 320176 332644 396514 969947 429707 105945 373899 677510 022400 596124 710767 155320 762978 308640 > 4²⁵⁴ [i]