MinT - Best Known (182−127, 182, s)-Nets in Base 4

Best Known (182−127, 182, s)-Nets in Base 4

(182−127, 182, 66)-Net over F₄ — Constructive and digital

Digital (55, 182, 66)-net over F₄, using

t-expansion [i] based on digital (49, 182, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(182−127, 182, 91)-Net over F₄ — Digital

Digital (55, 182, 91)-net over F₄, using

t-expansion [i] based on digital (50, 182, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(182−127, 182, 385)-Net in Base 4 — Upper bound on s

There is no (55, 182, 386)-net in base 4, because

1 times m-reduction [i] would yield (55, 181, 386)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 826301 502998 426922 105038 819685 416505 919635 459366 289523 942377 001027 437000 025901 645242 298934 890609 257257 947072 > 4¹⁸¹ [i]