MinT - Best Known (106, 241, s)-Nets in Base 4

Best Known (106, 241, s)-Nets in Base 4

(106, 241, 130)-Net over F₄ — Constructive and digital

Digital (106, 241, 130)-net over F₄, using

t-expansion [i] based on digital (105, 241, 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]

(106, 241, 144)-Net over F₄ — Digital

Digital (106, 241, 144)-net over F₄, using

t-expansion [i] based on digital (91, 241, 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]

(106, 241, 1178)-Net in Base 4 — Upper bound on s

There is no (106, 241, 1179)-net in base 4, because

1 times m-reduction [i] would yield (106, 240, 1179)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 230823 674097 149407 410735 891193 525610 753647 971139 066864 138762 807201 307212 258983 680275 987142 471826 584284 275021 568247 481076 491111 985883 237424 033880 > 4²⁴⁰ [i]