MinT - Best Known (216−99, 216, s)-Nets in Base 4

Best Known (216−99, 216, s)-Nets in Base 4

(216−99, 216, 130)-Net over F₄ — Constructive and digital

Digital (117, 216, 130)-net over F₄, using

t-expansion [i] based on digital (105, 216, 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]

(216−99, 216, 202)-Net over F₄ — Digital

Digital (117, 216, 202)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−99, 216, 2751)-Net in Base 4 — Upper bound on s

There is no (117, 216, 2752)-net in base 4, because

1 times m-reduction [i] would yield (117, 215, 2752)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2789 625620 860830 937596 521608 067976 203390 630036 868980 846452 051530 819974 821168 483812 162205 429610 962702 269295 602073 217789 009716 510531 > 4²¹⁵ [i]