MinT - Best Known (161, 161+40, s)-Nets in Base 4

Best Known (161, 161+40, s)-Nets in Base 4

(161, 161+40, 1068)-Net over F₄ — Constructive and digital

Digital (161, 201, 1068)-net over F₄, using

4¹ times duplication [i] based on digital (160, 200, 1068)-net over F₄, using
- trace code for nets [i] based on digital (10, 50, 267)-net over F₂₅₆, using
  - net from sequence [i] based on digital (10, 266)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(161, 161+40, 6524)-Net over F₄ — Digital

Digital (161, 201, 6524)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(161, 161+40, 3110896)-Net in Base 4 — Upper bound on s

There is no (161, 201, 3110897)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 328999 542135 182085 891533 098704 363001 879699 555252 431273 537987 439768 442973 132299 663156 524860 754890 821546 001735 282603 972216 > 4²⁰¹ [i]