MinT - Best Known (191−120, 191, s)-Nets in Base 4

Best Known (191−120, 191, s)-Nets in Base 4

(191−120, 191, 66)-Net over F₄ — Constructive and digital

Digital (71, 191, 66)-net over F₄, using

t-expansion [i] based on digital (49, 191, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(191−120, 191, 105)-Net over F₄ — Digital

Digital (71, 191, 105)-net over F₄, using

t-expansion [i] based on digital (70, 191, 105)-net over F₄, using
- net from sequence [i] based on digital (70, 104)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 70 and N(F) ≥ 105, using
    - Drinfeld modules of rank 1 [i]

(191−120, 191, 589)-Net in Base 4 — Upper bound on s

There is no (71, 191, 590)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 000490 446445 158440 647776 307909 666174 049085 189770 825833 739304 732795 718384 205413 750039 959897 955420 900174 088243 139540 > 4¹⁹¹ [i]