MinT - Best Known (151, 151+38, s)-Nets in Base 4

Best Known (151, 151+38, s)-Nets in Base 4

(151, 151+38, 1064)-Net over F₄ — Constructive and digital

Digital (151, 189, 1064)-net over F₄, using

4¹ times duplication [i] based on digital (150, 188, 1064)-net over F₄, using
- trace code for nets [i] based on digital (9, 47, 266)-net over F₂₅₆, using
  - net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(151, 151+38, 5828)-Net over F₄ — Digital

Digital (151, 189, 5828)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 151+38, 2576346)-Net in Base 4 — Upper bound on s

There is no (151, 189, 2576347)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 615660 228672 855598 683934 788153 145662 521893 746622 453669 378217 681761 906411 387568 569949 593540 605698 048199 254908 185004 > 4¹⁸⁹ [i]