MinT - Best Known (239−140, 239, s)-Nets in Base 4

Best Known (239−140, 239, s)-Nets in Base 4

(239−140, 239, 104)-Net over F₄ — Constructive and digital

Digital (99, 239, 104)-net over F₄, using

t-expansion [i] based on digital (73, 239, 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]

(239−140, 239, 144)-Net over F₄ — Digital

Digital (99, 239, 144)-net over F₄, using

t-expansion [i] based on digital (91, 239, 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]

(239−140, 239, 962)-Net in Base 4 — Upper bound on s

There is no (99, 239, 963)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 814124 214178 250869 891953 310481 700682 205950 798644 300211 750126 633567 731538 497459 543454 718740 673445 439121 947433 322611 878536 833063 472566 303236 193440 > 4²³⁹ [i]