MinT - Best Known (181, 181+52, s)-Nets in Base 4

Best Known (181, 181+52, s)-Nets in Base 4

(181, 181+52, 1052)-Net over F₄ — Constructive and digital

Digital (181, 233, 1052)-net over F₄, using

4¹ times duplication [i] based on digital (180, 232, 1052)-net over F₄, using
- trace code for nets [i] based on digital (6, 58, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(181, 181+52, 3752)-Net over F₄ — Digital

Digital (181, 233, 3752)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(181, 181+52, 874067)-Net in Base 4 — Upper bound on s

There is no (181, 233, 874068)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 190 538513 721541 660413 621837 143358 243646 520657 953903 129843 946551 855841 875839 209204 762842 931493 629266 278096 118683 321759 916915 963975 115564 267800 > 4²³³ [i]