MinT - Best Known (21, 72, s)-Nets in Base 4

Best Known (21, 72, s)-Nets in Base 4

(21, 72, 34)-Net over F₄ — Constructive and digital

Digital (21, 72, 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]

(21, 72, 44)-Net over F₄ — Digital

Digital (21, 72, 44)-net over F₄, using

net from sequence [i] based on digital (21, 43)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 44, using
  - a curve from the manYPoints database [i]

(21, 72, 115)-Net in Base 4 — Upper bound on s

There is no (21, 72, 116)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁷², 116, S₄, 51), but
- the linear programming bound shows that MÂ â‰¥ 10188 107061 418334 440590 089803 281735 251458 760523 288912 636635 545187 112356 798015 053544 554496 / 445 994962 135541 633265 915937 778940 613693 671225 > 4⁷² [i]