MinT - Best Known (216−101, 216, s)-Nets in Base 4

Best Known (216−101, 216, s)-Nets in Base 4

(216−101, 216, 130)-Net over F₄ — Constructive and digital

Digital (115, 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]

(216−101, 216, 190)-Net over F₄ — Digital

Digital (115, 216, 190)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−101, 216, 2479)-Net in Base 4 — Upper bound on s

There is no (115, 216, 2480)-net in base 4, because

1 times m-reduction [i] would yield (115, 215, 2480)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2824 028298 300041 962070 066511 975908 538579 690759 679938 472862 348608 904884 904823 266019 228951 453095 942328 664227 520361 891864 929070 978536 > 4²¹⁵ [i]