MinT - Best Known (182−42, 182, s)-Nets in Base 4

Best Known (182−42, 182, s)-Nets in Base 4

(182−42, 182, 1040)-Net over F₄ — Constructive and digital

Digital (140, 182, 1040)-net over F₄, using

4² times duplication [i] based on digital (138, 180, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 45, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(182−42, 182, 2552)-Net over F₄ — Digital

Digital (140, 182, 2552)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−42, 182, 477759)-Net in Base 4 — Upper bound on s

There is no (140, 182, 477760)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 37 577895 569271 013731 743376 884547 978585 229498 568005 492635 003975 443991 847133 227274 226446 409278 104609 385914 820869 > 4¹⁸² [i]