MinT - Best Known (254−127, 254, s)-Nets in Base 4

Best Known (254−127, 254, s)-Nets in Base 4

(254−127, 254, 130)-Net over F₄ — Constructive and digital

Digital (127, 254, 130)-net over F₄, using

t-expansion [i] based on digital (105, 254, 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]

(254−127, 254, 178)-Net over F₄ — Digital

Digital (127, 254, 178)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−127, 254, 2068)-Net in Base 4 — Upper bound on s

There is no (127, 254, 2069)-net in base 4, because

1 times m-reduction [i] would yield (127, 253, 2069)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 212 451527 648066 934336 419061 495973 307668 149041 101640 384649 899928 262947 674391 498198 857784 756261 362037 271174 854619 621743 938734 195461 447993 362574 221418 526720 > 4²⁵³ [i]