MinT - Best Known (240−140, 240, s)-Nets in Base 4

Best Known (240−140, 240, s)-Nets in Base 4

(240−140, 240, 104)-Net over F₄ — Constructive and digital

Digital (100, 240, 104)-net over F₄, using

t-expansion [i] based on digital (73, 240, 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]

(240−140, 240, 144)-Net over F₄ — Digital

Digital (100, 240, 144)-net over F₄, using

t-expansion [i] based on digital (91, 240, 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]

(240−140, 240, 982)-Net in Base 4 — Upper bound on s

There is no (100, 240, 983)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 176121 515758 212742 877285 739299 122889 058575 817793 141132 990757 565727 832348 056231 463038 979835 042233 532814 542734 225639 309780 586892 089312 675103 669579 > 4²⁴⁰ [i]