MinT - Best Known (223−103, 223, s)-Nets in Base 4

Best Known (223−103, 223, s)-Nets in Base 4

(223−103, 223, 130)-Net over F₄ — Constructive and digital

Digital (120, 223, 130)-net over F₄, using

t-expansion [i] based on digital (105, 223, 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]

(223−103, 223, 203)-Net over F₄ — Digital

Digital (120, 223, 203)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−103, 223, 2721)-Net in Base 4 — Upper bound on s

There is no (120, 223, 2722)-net in base 4, because

1 times m-reduction [i] would yield (120, 222, 2722)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45 607645 145207 772082 205905 405091 410906 485165 657305 061633 833881 715917 409914 724948 791248 759499 972146 813376 035030 172079 198486 908373 210560 > 4²²² [i]