MinT - Best Known (190−46, 190, s)-Nets in Base 4

Best Known (190−46, 190, s)-Nets in Base 4

(190−46, 190, 1032)-Net over F₄ — Constructive and digital

Digital (144, 190, 1032)-net over F₄, using

4² times duplication [i] based on digital (142, 188, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 47, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(190−46, 190, 2069)-Net over F₄ — Digital

Digital (144, 190, 2069)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(190−46, 190, 295696)-Net in Base 4 — Upper bound on s

There is no (144, 190, 295697)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 462657 901294 407996 321828 005832 862342 851595 825170 438351 044648 427490 961121 994322 824651 366521 668062 975494 447746 962688 > 4¹⁹⁰ [i]