MinT - Best Known (91, 91+145, s)-Nets in Base 4

Best Known (91, 91+145, s)-Nets in Base 4

(91, 91+145, 104)-Net over F₄ — Constructive and digital

Digital (91, 236, 104)-net over F₄, using

t-expansion [i] based on digital (73, 236, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(91, 91+145, 144)-Net over F₄ — Digital

Digital (91, 236, 144)-net over F₄, using

net from sequence [i] based on digital (91, 143)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
  - Drinfeld modules of rank 1 [i]

(91, 91+145, 792)-Net in Base 4 — Upper bound on s

There is no (91, 236, 793)-net in base 4, because

1 times m-reduction [i] would yield (91, 235, 793)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3307 525827 849678 443690 897513 157153 247170 953200 257485 711888 666875 468621 207381 559907 379278 423325 969976 289540 101386 743965 649548 737853 681243 537500 > 4²³⁵ [i]