MinT - Best Known (230−103, 230, s)-Nets in Base 4

Best Known (230−103, 230, s)-Nets in Base 4

(230−103, 230, 130)-Net over F₄ — Constructive and digital

Digital (127, 230, 130)-net over F₄, using

t-expansion [i] based on digital (105, 230, 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]

(230−103, 230, 230)-Net over F₄ — Digital

Digital (127, 230, 230)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−103, 230, 3300)-Net in Base 4 — Upper bound on s

There is no (127, 230, 3301)-net in base 4, because

1 times m-reduction [i] would yield (127, 229, 3301)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 745015 456670 843501 912325 500960 717972 794265 164199 462233 220558 771367 460298 537178 695817 089073 056098 856626 406928 528743 927797 042199 835139 000912 > 4²²⁹ [i]