MinT - Best Known (66−43, 66, s)-Nets in Base 4

Best Known (66−43, 66, s)-Nets in Base 4

(66−43, 66, 34)-Net over F₄ — Constructive and digital

Digital (23, 66, 34)-net over F₄, using

t-expansion [i] based on digital (21, 66, 34)-net over F₄, using
- net from sequence [i] based on digital (21, 33)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
    - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(66−43, 66, 45)-Net over F₄ — Digital

Digital (23, 66, 45)-net over F₄, using

net from sequence [i] based on digital (23, 44)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 23 and N(F) ≥ 45, using
  - a curve from the manYPoints database [i]

(66−43, 66, 190)-Net in Base 4 — Upper bound on s

There is no (23, 66, 191)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁶⁶, 191, S₄, 43), but
- the linear programming bound shows that MÂ â‰¥ 28 766535 420054 304848 397361 421684 986456 320614 942528 963784 752261 977481 718335 232020 438414 046131 126272 000000 / 5209 403279 129645 739501 754543 221181 850628 166933 877437 442223 389477 > 4⁶⁶ [i]