MinT - Best Known (203−91, 203, s)-Nets in Base 4

Best Known (203−91, 203, s)-Nets in Base 4

(203−91, 203, 130)-Net over F₄ — Constructive and digital

Digital (112, 203, 130)-net over F₄, using

t-expansion [i] based on digital (105, 203, 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]

(203−91, 203, 205)-Net over F₄ — Digital

Digital (112, 203, 205)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−91, 203, 2925)-Net in Base 4 — Upper bound on s

There is no (112, 203, 2926)-net in base 4, because

1 times m-reduction [i] would yield (112, 202, 2926)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 630289 431430 877887 435791 206374 267161 496518 505630 247855 499909 376617 711589 647978 427596 854066 549021 007060 877708 802019 714425 > 4²⁰² [i]