MinT - Best Known (231−105, 231, s)-Nets in Base 4

Best Known (231−105, 231, s)-Nets in Base 4

(231−105, 231, 130)-Net over F₄ — Constructive and digital

Digital (126, 231, 130)-net over F₄, using

t-expansion [i] based on digital (105, 231, 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]

(231−105, 231, 220)-Net over F₄ — Digital

Digital (126, 231, 220)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−105, 231, 3060)-Net in Base 4 — Upper bound on s

There is no (126, 231, 3061)-net in base 4, because

1 times m-reduction [i] would yield (126, 230, 3061)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 025100 395966 380227 350823 639636 846493 812303 125719 641942 184631 217054 905182 587332 211266 547185 098135 504613 856935 111831 339592 524821 967509 098503 > 4²³⁰ [i]