MinT - Best Known (131, 131+42, s)-Nets in Base 4

Best Known (131, 131+42, s)-Nets in Base 4

(131, 131+42, 1032)-Net over F₄ — Constructive and digital

Digital (131, 173, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (130, 172, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 43, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(131, 131+42, 1887)-Net over F₄ — Digital

Digital (131, 173, 1887)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+42, 263736)-Net in Base 4 — Upper bound on s

There is no (131, 173, 263737)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 143 345007 542100 665875 521508 979701 302969 405812 761300 580687 698373 251603 334993 365660 652039 398740 222694 710112 > 4¹⁷³ [i]