MinT - Best Known (241−59, 241, s)-Nets in Base 4

Best Known (241−59, 241, s)-Nets in Base 4

(241−59, 241, 1032)-Net over F₄ — Constructive and digital

Digital (182, 241, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (181, 240, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 60, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(241−59, 241, 2404)-Net over F₄ — Digital

Digital (182, 241, 2404)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−59, 241, 373713)-Net in Base 4 — Upper bound on s

There is no (182, 241, 373714)-net in base 4, because

1 times m-reduction [i] would yield (182, 240, 373714)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 121884 081377 191316 182419 122343 494991 515862 111577 517060 664218 298209 804261 564697 712688 535024 405408 837430 815154 210473 655498 284301 102496 826088 903792 > 4²⁴⁰ [i]